The original Saw. They eventually got a bad reputation as stupid exploitation movies that were nothing but senseless gore, which is because over half the series was. But that's only after all the writers and directors and shit changed. The first Saw movie was fucking amazing, doesn't have a lot of gore and blows my mind every time. It's such a unique movie in the way it tells its story and everything comes together at the end and the last fifteen minutes of it are my favorite part of any movie. Definitely invest in watching the original Saw no matter what you've heard or even seen about the later mvoies in that series, because that's like comparing Survivor: Borneo to Surivor: Redemption Island.
Haven't saw The Ring in full, may give that a watch soon!
Seen all the Saw movies and I agree it's best of them all. I once saw a fan edit of all the series (the main plots taken out of the films and condensed into a 2hr and a half film) it was a great way of piecing the entire story together!